09/09/2007, 12:21 AM

The oldest reference I know of is Koch [2], which according to Bennett [1], was the first to consider using Bell-Carleman matrices to derive the "regular" formal series of a continuous iteration of a function. But since we're talking about different things, I can see how your reference can be older, since you're talking about the series themselves, not finding them through matrices. Bennett also mentions Koenigs, so he obviously knew of him.

[1] Albert A. Bennett, The Iteration of Functions of one Variable, The Annals of Mathematics, 2nd Ser., Vol. 17, No. 1, pp. 23-60, (Sep. 1915).

[2] H. v. Koch, Bil. t. Sv. Vet. Ak. Hand. 1, Math. 25, m\'em. no. 5, pp. 1-24, (1900).

[1] Albert A. Bennett, The Iteration of Functions of one Variable, The Annals of Mathematics, 2nd Ser., Vol. 17, No. 1, pp. 23-60, (Sep. 1915).

[2] H. v. Koch, Bil. t. Sv. Vet. Ak. Hand. 1, Math. 25, m\'em. no. 5, pp. 1-24, (1900).